Orthogonal projectors and the method of symmetrical components for multiphase electromagnetic systems

A method of constructing orthogonal operator projectors for expanding a vector-function (for example, the voltages and currents of a multiphase electromagnetic system) into orthogonal components, symmetrical with respect to one of the elements of a finite multiplicative cyclic group of linear operators, is proposed. This method is a mathematical generalization of the method of current and voltage symmetrical components. Translated from Izmeritel’naya Tekhnika, No. 1, pp. 42–47, January, 2009.     

A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations

This paper presents a variational multiscale residual-based stabilized finite element method for the incompressible Navier–Stokes equations. Structure of the stabilization terms is derived based on the two level scale separation furnished by the variational multiscale framework. A significant feature of the new method is that the fine scales are solved in a direct nonlinear fashion, and a definition of the stabilization tensor τ is derived via the solution of the fine-scale problem. A computationally economic procedure is proposed to evaluate the advection part of the stabilization tensor. The new method circumvents the Babuska–Brezzi (inf–sup) condition and yields a stable formulation for high Reynolds number flows. A family of equal-order pressure-velocity elements comprising 4-and 10-node tetrahedral elements and 8- and 27-node hexahedral elements is developed. Convergence rates are reported and accuracy properties of the method are presented via the lid-driven cavity flow problem.     

A meshless local boundary integral equation method for two-dimensional steady elliptic problems

A novel meshless local boundary integral equation (LBIE) method is proposed for the numerical solution of two-dimensional steady elliptic problems, such as heat conduction, electrostatics or linear elasticity. The domain is discretized by a distribution of boundary and internal nodes. From this nodal points’ cloud a “background” mesh is created by a triangulation algorithm. A local form of the singular boundary integral equation of the conventional boundary elements method is adopted. Its local form is derived by considering a local domain of each node, comprising by the union of neighboring “background” triangles. Therefore, the boundary shape of this local domain is a polygonal closed line. A combination of interpolation schemes is taken into account. Interpolation of boundary unknown field variables is accomplished through boundary elements’ shape functions. On the other hand, the Radial Basis Point Interpolation Functions method is employed for interpolating the unknown interior fields. Essential boundary conditions are imposed directly due to the Kronecker delta-function property of the boundary elements’ interpolation functions. After the numerical evaluation of all boundary integrals, a banded stiffness matrix is constructed, as in the finite elements method. Several potential and elastostatic benchmark problems in two dimensions are solved numerically. The proposed meshless LBIE method is also compared with other numerical methods, in order to demonstrate its efficiency, accuracy and convergence.     

楼宇设备工程中结构声功率预测的平均特征值法

机器透过安装点进入到支撑结构的总功率是反映结构噪声的重要物理量。导纳方法提供正确预测该值的途径,但这种方法涉及到太多的物理量,缺乏实用性。寻找简便的近似预测方法有着重要的意义。本文以特征值理论为基础,针对楼宇设备工程中源导纳远大于地板导纳的场合,给出简便的近似预测公式。以典型风机为例,将本文的方法与其他的较复杂近似预测方法比较。结果表明,本文所给出的简便方法与精确值的误差约为4dB,比其它近似方法具有更好的预测准确度。     

New system of standard exergies of chemical elements. I. Standard exergies of ionogen elements

A system of standard exergies of chemical elements and individual substances is proposed that is based on the choice of the aqueous phase of the World Ocean — “sea water” — as an environmental niche and the choice of simple (one-element) cations and anions existing in it — with account for their concentrations — as reference substances for their constituting ionogen elements. Standard exergies of ionogen elements are calculated. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 516–520, May–June, 1998.     

Development of eight-node quadrilateral membrane elements using the area coordinates method

 Two eight-node quadrilateral elements, namely, AQ8-I and AQ8-II, have been developed using the quadrilateral area coordinate and generalized conforming methods. Some appropriate examples were employed to evaluate the performance of the proposed elements. The numerical results show that the proposed elements are superior to the standard eight-node isoparametric element, thereafter called Q8. This is because the former does not only possess the same accuracy as the latter when regular meshes are employed for analysis, but is also very insensitive to mesh distortion, for which the Q8 element can not handle. It has also been demonstrated that the area coordinate method is an efficient tool for developing simple, effective and reliable serendipity plane membrane elements. Received 11 August 1999     

Two-dimensional analysis of anisotropic crack problems using coupled meshless and fractal finite element method

This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with fractal the finite element method (FFEM) for analyzing homogeneous, anisotropic, and two dimensional linear-elastic cracked structures subjected to mixed-mode (modes I and II) loading conditions. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprises both the element-free Galerkin and the finite element shape functions, satisfies the consistency condition thus ensuring convergence of the proposed coupled EFGM-FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no structured mesh or special enriched basis functions are necessary and no post-processing (employing any path independent integrals) is needed to determine fracture parameters such as stress-intensity factors (SIFs) and T − stress. The numerical results based on all four orthotropic cases show that SIFs and T − stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack length to width ratio on the quality of the numerical solutions.     

An average stress strain approach to creep analysis of RC uncracked elements

The paper presents a method which enables us to perform creep analysis of RC elements with uncracked cross-sections relying on the evaluation of an average stress strain state in a sense to fulfill Volterra’s integral term in time interval elapsed after loading and the prediction of an actual state at the time considered. The analytically derived expressions for time-dependent stresses, strains and curvatures are very simple, being gained by a newly proposed relation for the ageing coefficient, constitutive law for creep and the classical formulae of strength of materials. The method proposed is mathematically tractable, as well as accounting for the variation of elastic modulus. A validity of the method proposed was proven by direct calculation of the time-dependent parameters in the analysis of various RC elements. The approach gives exact values of the time-dependent stress strain state as those determined using the age-adjusted effective modulus method involving a sophisticated relaxation procedure. The method does not require the introduction of the fictitious restraining actions dramatically simplifying computation and could be used as a simple alternative approach for the exact analysis of RC uncracked elements. Numerical examples and methodology for applicability to RC structures/elements were also developed.     

Nondestructive testing of composite and metallic pipes by the method of electronic shearography

A method for nondestructive testing of the quality of structures based on the application of electronic shearography is proposed. We present results of monitoring of the elements of pipes produced by welding and gluing. The presented results of investigations show that the developed technology can be applied under the conditions of manufacturing. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 66–70, July–August, 2007.     

Calculation of natural and forced vibrations of a piping system. Part 1. Analysis of vibrations of a 3D beam system

Dynamic behavior of piping as a beam system has been analyzed with the use of the dynamic stiffness method. According to this method, the equations describing the relation between unknown parameters are written by the method of initial parameters, therefore, the solution procedure is similar to that for a static problem. It is shown that for curvilinear beams it is simpler and more efficient to apply a model that consists of straight segments and inertia-free rotation elements. To determine natural frequencies of 3D beam systems, it is proposed to use a method of disconnection of displacements, which makes it possible to discern the frequencies corresponding to different vibration modes (transverse, longitudinal, etc.). The approach allows a correct simulation of the system behavior under forced vibrations induced by a harmonic exciting force. __________ Translated from Problemy Prochnosti, No. 1, pp. 79–93, January–February, 2007.     

Fracture analysis in 2D magneto–electro–elastic media by the boundary element method

An integral formulation for 2D cracked infinite anisotropic magneto–electro–elastic media is presented. Based on the method proposed by Garcia-Sanchez et al. (Comput Struct 83: 804–820, 2005), the hypersingular kernels are analytically transformed into weakly singular and regular integrals with known analytical solution. Special quadratic discontinuous crack tip elements are employed to model the singular characteristics of the stresses, electric displacements and magnetic inductions. The extended stress intensity factors at the crack tips are calculated using the extended discontinuous displacements at crack tip elements based on one point extended displacement formulation. Some results for curved cracks in magneto–electro–elastic media are also presented.     

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner–Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.     

Comparison of the methods of boundary and near-boundary elements for the solution of problems in the theory of elasticity

The method of near-boundary elements is now a commonly used tool of the mechanics of deformable body. This method is based on the reduction of an original boundary-value problem to integral equations given in the external near-boundary zone (unlike the method of boundary elements with integral equations defined on the boundary of the region). The near-boundary zone is split into near-boundary elements in the form of curvilinear polygons. We perform the theoretical and numerical analysis of various aspects of the methods of boundary and near-boundary elements. We show that the accuracy of the numerical evaluation of the components of the vector of displacements attained by using the method of near-boundary elements is higher than that typical of the method of boundary elements. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv; Carpathian Department of the Subbotin Institute of Geophysics, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 3, pp. 50–56 May–June, 1997.     

Measurement of the quality of laser beams by methods of fourier optics

A new method of determining the magnitude of M², the coefficient of exceedance of the diffraction limit of the divergence of a laser beam, based on the principles of Fourier optics is proposed. By means of the new method, it is possible to substantially simplify the design of the measuring transducer and expand the types of devices that may be used to measure the parameters of laser beams. An experimental comparison of the proposed method with the method regulated by ISO Standard 11146 is conducted. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 42–45, October, 2006.     

Strength of cracked structural elements healed by injection methods

We develop a method aimed at the evaluation of the residual strength of cracked structural elements strengthened with the help of injection technologies. The basic parameters responsible for the efficiency of injection are established and possible ways of optimization of the proposed technology are indicated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 6, pp. 60–64, November–December, 2005.     

Prospects of the rolling method for measuring linear displacements and dimensions

This article examines aspects of the interaction of a measurement disk with a specimen through a flexible elastic element. A method is proposed for determining the main parameters of measuring devices with allowance for the displacement of the neutral axis of the elastic element as it is bent by the disk. Examples are presented to illustrate the use of the rolling method in measuring instruments with flexible elements. Translated from Izmeritel'naya Tekhnika, No. 5, pp 23–24, May, 1996.     

A model of a magnetomodulation converter

A model of a magnetomodulation converter in which the remagnetization of the sensitive elements is approximated by a piecewise-linear function is proposed. Translated from Izmeritel’naya Tekhnika, No. 1, pp. 47–51, January, 2009.     

Stress analysis for multilayered coating systems using semi-analytical BEM with geometric non-linearities

For a long time, most of the current numerical methods, including the finite element method, have not been efficient to analyze stress fields of very thin structures, such as the problems of thin coatings and their interfacial/internal mechanics. In this paper, the boundary element method for 2-D elastostatic problems is studied for the analysis of multi-coating systems. The nearly singular integrals, which is the primary obstacle associated with the BEM formulations, are dealt with efficiently by using a semi-analytical algorithm. The proposed semi-analytical integral formulas, compared with current analytical methods in the BEM literature, are suitable for high-order geometry elements when nearly singular integrals need to be calculated. Owing to the employment of the curved surface elements, only a small number of elements need to be divided along the boundary, and high accuracy can be achieved without increasing more computational efforts. For the test problems studied, very promising results are obtained when the thickness of coated layers is in the orders of 10⁻⁶–10⁻⁹, which is sufficient for modeling most coated systems in the micro- or nano-scales.     

Elastic Wave Propagation in a Class of Cracked,Functionally Graded Materials by BIEM

Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson’s ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ (x)=μ ₀ exp (2ax ₂), where μ ₀ is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green’s function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case     

基于测深侧扫声呐的DOA估计算法研究

针对测深侧扫声呐进行波达方向(Direction of Arrival, DOA)估计时会受到阵元幅度、相位误差及低信噪比影响的问题,提出一种改进的波束域加权子空间拟合算法。首先,采用总体最小二乘-旋转不变子空间算法进行回波方向预估计;其次,将连续线阵划分为多个子阵,并将各个子阵在预估计方向做加权波束形成;再次,采用加权子空间拟合(Weighted Subspace Fitting, WSF)算法构造代价函数;最后,采用阻尼牛顿法求解得到高精度的DOA估计结果。仿真结果表明,文中所提算法在阵元出现幅度相位误差条件下的角度估计均方误差相对于WSF算法减少了约0.03°。海试数据分析结果表明,文中所提算法的测深点均方误差整体优于WSF算法,其相对测深精度提高了约9.8个百分点。以上分析结果表明,文中所提算法整体优于WSF算法,可以实现在阵元幅度相位误差及低信噪比情况下的高精度DOA估计。